Darion Rackley's jumper with :51 left to play pulled Jacksonville State (0-4) within six at 79-73, but after Luther Page made one of two free throws, his block on a Brian Williams layup attempt eight seconds later essentially clinched the win for the Hornets.
Alabama State (2-2) opened up a 16-point lead about halfway through the first half but the Gamecocks closed the half with a 14-4 run, entering halftime trailing 44-43.
Terrance LeFlore hit 3-pointers on back-to-back possessions, his only points of the game, to push the Hornets' lead back to 10, 68-58, with 9:59 remaining. Jacksonville State never again got closer than within five.
DeMarcus Robinson added 15 points and Luther Page 11 for the Hornets.
Rackley led Jacksonville State with 23. Williams and Nick Cook each had 16.